Listen
[tex]r=\frac{V_d+V_c}{V_c}[/tex]
What is this formula used to calculate?
A) Radius
B) Volume
C) Compression ratio
D) Mass ratio
Answer (1)
The formula r = V c V d + V c calculates the compression ratio, which is the ratio of the maximum volume to the minimum volume in a cylinder.
Simplify the formula: r = V c V d + 1 .
Recognize V d as displacement volume and V c as clearance volume.
Compression ratio is defined as V c V d + V c .
Therefore, the formula calculates the compression ratio: C .
Explanation
Understanding the Formula The formula given is r = V c V d + V c . We need to determine what this formula is used to calculate from the given options.
Simplifying the Formula Let's simplify the formula: r = V c V d + V c V c = V c V d + 1 Here, V d represents the displacement volume and V c represents the clearance volume.
Understanding Compression Ratio The compression ratio is defined as the ratio of the maximum volume to the minimum volume in a cylinder. The maximum volume is the sum of the displacement volume and the clearance volume, i.e., V d + V c . The minimum volume is the clearance volume, V c . Therefore, the compression ratio is given by: V c V d + V c
Conclusion Comparing the given formula r = V c V d + V c with the definition of the compression ratio, we can conclude that the formula calculates the compression ratio.
Examples
In internal combustion engines, the compression ratio is a crucial parameter that affects the engine's efficiency and performance. A higher compression ratio generally leads to better fuel efficiency and increased power output, but it also increases the risk of engine knocking. The formula r = V c V d + V c allows engineers to calculate the compression ratio based on the engine's design parameters, where V d is the displacement volume and V c is the clearance volume. For example, if an engine has a displacement volume of 400 cc and a clearance volume of 50 cc, the compression ratio would be r = 50 400 + 50 = 9 .
